A.M Kassim, T. Yasuno, Sivaraos, H.I Jaafar,
Copyright © 2007 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. xx, n. x
oscillator interact with the sensory feedback signals from the musculoskeletal systems [13-14]. Then, by using the concept of
walking motion control model suggested by Taga, Kimura proposed a method of structuring the coupling of neural and
mechanical systems for the implementation of autonomous adaption through the irregular terrain [15]. Besides that, Son et al.
proposed a CPG model including the motor dynamic characteristics of an actuator for the purpose of implementing
generation adaptive gait patterns for a quadruped robot under various environments [16]. Meanwhile, Kondo et al. has
developed the quadruped hopping robot which is used central pattern generators CPGs as pattern generator in order to
generate the continuous jumping performance while control the stability of body balance [17-19].
In this paper, the generation of moving and braking motion control for the developed quadruped hopping robot while
jumping continuously on two-dimensional space is proposed. Here, the reference height control system is applied to control
the reference height for each leg independently [20-22]. Therefore, the differences height of front legs and back legs to
generate the moving performance and correcting the body posture which has inclined to make the quadruped hopping
robot jump vertically can be created. On the other hand, the effectiveness of Central Pattern GeneratorCPG network to keep
the stability of quadruped hopping robot an d avoiding it from tumble ahead also evaluated.
II. Developed Hopping Robot
II.1. Robot Construction
Figure 1 shows the developed quadruped hopping robot construction overall length is 49cm, overall width is 49cm,
overall height is 37cm and the total weight is 9.1kg. The quadruped hopping robot consists of the legs. Each leg is
composed with a DC geared motor 12V, 200min
-1
, 0.0098Nm, a crank and a spring attached to the crankshaft. Then, each leg is
connected to the shared platform.
Fig. 1 Quadruped hopping robot
The developed quadruped hopping robot is developed by a DC geared motor which is driven by using DC amplifier and
connect to the crank which used to push the platform.
Fig. 2 Hopping mechanism
As shown in Figure 2, the hopping mechanism of the quadruped hopping robot can be achieved respectively. Here,
the motor torque is converted to the periodic force to the spring and make a periodical hopping motion of hopping robot as the
basis of the principle hopping motion. The continuous hopping of quadruped hopping robot could be generated by using floor
repulsive force when the suitable force was applied to the spring at the suitable time.
II.2. Experimental Setup
Figure 3 shows the experimental setup to evaluate the quadruped hopping robot. The proposed CPG network is
expressed using a MATLABSimulink model on a host computer. Then the model, built by a Realtime workshop, is
downloaded to xPC target computer. The xPC target computer is run by using a realtime OS. The position of the center and each
leg are measured using ultrasonic sensors which are used as sensory feedback signals of the CPG. The sampling time is set for
controlling this experimental setup is 0.01s.
Fig. 3 Experimental setup
III. System Configuration
III.1. CPG Model
Figure 4 shows the conventional CPG model which is
A.M Kassim, T. Yasuno, Sivaraos, H.I Jaafar,
Copyright © 2007 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. xx, n. x
proposed by Taga[9]. The CPG model is modified to a block diagram of the CPG model which is shown in Figure 5. Here, the
inhibitory unit of the CPG includes the mechanical dynamics of the leg. Parameters u
e
and u
i
denotes the internal state of the excitatory unit and the inhibitory unit, b and c denotes the
intrinsic excitatory and inhibitory coupling parameter, a denotes the excitatory coupling factor while B
denotes the constant bias input. The output of the inhibitory unit corresponds to the
platform position of each leg and is applied to the excitatory unit through a nonlinear function tan
−1
u
i
and the feedback gain b which formulated as
Fig. 4 Conventional CPG model
Fig. 5. Block diagram of CPG model.
where f is the mechanical dynamics of the hopping robot’s leg, K
a
is the gain constant of the DC amplifier and d is the external disturbance which is the floor repulsive force in this
case. By arbitrarily hanging the coupling parameters a, b, c, the time constant
τ
e
and the mechanical dynamics of the hopping robot, the CPG can change the amplitude and the frequency of
internal states u
e
and u
i
. III.2.
Reference height control algorithm Fig. 6 shows the block diagram of the reference height
control algorithm for one leg of developed tripod hopping robot. This block diagram is built by using MATLABSimulink tool.
This system consists of maximum height detector, the PI controller and the CPG. By using the proposed control algorithm,
the tripod hopping robot can keep the hopping motion and control the hopping height to achieve the reference hopping
height by adding a feedback loop through a fixed gain PI controller. The joint actuator is driven by the control system in
order to realize the reference hopping position generated by the PI controller on each leg.
Deduction of sensory feedback signal h
max
of the ultrasonic sensors on each legs from the reference height h
reff
gives the value of steady state error h
diff
which represents the command signal. In control engineering, a PI controller is a feedback
controller which drives the plant to be controlled with a weighted sum of error h
diff
and integral of that value. The integral term in PI controller causes the steady state error to be zero for a step
input.
Fig. 6. Block diagram of reference height control system
III.3. Moving and Braking Motion
Here, the proposed moving and braking method which is used in order to control the moving and braking system for
quadruped hopping robot is mentioned. The reference height control system is applied in order to set the desired hopping
height for each leg for quadruped hopping robot. The reference height control system is used to create the differences height of
front legs and back legs to make body posture incline ahead for moving performance. In addition, the body posture of
quadruped hopping robot will be corrected in order to jump vertically again by set the reference jumping height for each leg
to same reference height. Figure 7 shows the moving and braking condition. The correction of body posture which has inclined by
setting the reference height for all legs to 20cm could make the quadruped hopping robot jump in one dimension called braking
motion.
A.M Kassim, T. Yasuno, Sivaraos, H.I Jaafar,
Copyright © 2007 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. xx, n. x
The whole experiment is conducted in 60sec which in the first 10sec period, the reference hopping height is set for all legs
to 20cm in order to maintain the oscillation of hopping performances, in advance. Then, after 10sec until 40sec, the
moving performance is set where leg 2 and 4 is set as back leg and the reference height is set to 21cm while leg 1 and 3 is set as
front leg which the reference height is set to 18 cm. Therefore, started from 40sec to 50sec, the proposed braking motion
performance where all legs will be set to same reference height at 20cm. After that, the moving performance is set again from 50sec
to 60sec to evaluate the effectiveness of proposed braking motion control method.
Moving motion Braking motion
Figure 7 Robot posture for moving and braking motion
III.4. CPG Networks
The quadruped hopping robot can continuously jump by applying the same periodic force to each spring of robot and the
cooperative oscillation among the CPGs is required. By using the ring-and-cross type CPG network, the stable, continuous and
rhythmical hopping performance is obtained. In addition, Figure 8 shows the reference height control system is included into CPG
model in each leg in order to control the hopping height of each leg independently.
Figure 8 Ring cross type CPG networks
IV. Experimental results
